Effective series expansions are derived for the evaluation of the single integral in the potential of a submerged source which moves with constant velocity, when the source and field point are in the same longitudinal centerplane. In conjunction with the polynomial approximations for the double integral component which have been derived in Part 1 of this work, the present results facilitate the computation of the source potential or Green function. Three complementary domains of the centerplane are considered, with different expansions developed for use in each domain. The principal expansion is based on a Neumann series which is effective for small or moderate distances from the origin, except in a thin region near the free surface. To deal with the latter domain an asymptotic expansion is derived in ascending powers of the vertical coordinate. Both of these expansions are refined by subtracting a simpler component with the same behavior at the origin, and relating this component to Dawson's integral. Special algorithms for the evaluation of the latter function are presented in the Appendix. The third and final expansion, based upon the method of steepest descents, is effective at large distances from the origin. This asymptotic series is derived by a systematic recursive scheme to permit an arbitrary order of the approximation. Used in conjunction with the first two expansions, this permits the single integral to be evaluated with an absolute accuracy of six decimals throughout the centerplane.